Alpha-olefin dimers typified by 4-methyl-1-pentene (including codimers; the same applies hereinafter) are utilized as monomers for the production of polyolefins. Many basic catalysts have been conventionally proposed as catalysts for the production of corresponding dimers through α-olefin dimerization reactions (including codimerization reactions; the same applies hereinafter). Especially, many catalysts obtained by supporting an alkali metal on a support mainly containing an anhydrous potassium compound have been used.
On these catalysts, studies for further enhancing the activity and selectivity to target substances have been made continuously. Also, due to their insufficient catalyst lifetime despite high initial activity, studies for extending the catalyst lifetime have been also made continuously. For example, Japanese Patent Application Laid-Open (JP-A) Nos. S58-114737, H3-42043, H7-222927, 2006-326418, and 2008-149275, and U.S. Pat. No. 5,081,094 describe to adjust physical properties of anhydrous potassium compounds or supports to be used so that the improvements in activity, selectivity and catalyst lifetime are pursued.